Question 1

If the sum of squared residuals is zero, then the:

Accepted Answer

A) coefficient of determination must be 1.0. 
B) coefficient of correlation must be 1.0. 
C) coefficient of determination must be 0.0. 
D) coefficient of correlation must be 0.0. 
A) coefficient of determination must be 1.0. 
B) coefficient of correlation must be 1.0. 
C) coefficient of determination must be 0.0. 
D) coefficient of correlation must be 0.0.

Question 2

Which of the following statements best describes why a linear regression is also called a least squares regression model?

Accepted Answer

A) A linear regression is also called a least squares regression model because the regression line is calculated by minimizing the square of the difference between each actual x data value and the predicted x value. 
B) A linear regression is also called a least squares regression model because the regression line is calculated by minimizing the sum of the difference between each actual y data value and the predicted y value. 
C) A linear regression is also called a least squares regression model because the regression line is calculated by minimizing the square of each actual y data value and the predicted y value. 
D) why a A linear regression is also called a least squares regression model because the regression line is calculated by minimizing the sum of the square of the differences between each actual y data value and the predicted y value. 
A) A linear regression is also called a least squares regression model because the regression line is calculated by minimizing the square of the difference between each actual x data value and the predicted x value. 
B) A linear regression is also called a least squares regression model because the regression line is calculated by minimizing the sum of the difference between each actual y data value and the predicted y value. 
C) A linear regression is also called a least squares regression model because the regression line is calculated by minimizing the square of each actual y data value and the predicted y value. 
D) why a A linear regression is also called a least squares regression model because the regression line is calculated by minimizing the sum of the square of the differences between each actual y data value and the predicted y value.

Question 3

When the actual values y of a dependent variable and the corresponding predicted values $\ddot { p }$ are the same, the standard error of estimate, $S _ { \varepsilon }$ , will be -1.0.

Accepted Answer

A) True 
 B)False

Question 4

A direct relationship between an independent variable x and a dependent variably y means that x and y move in the same directions.

Accepted Answer

A) True 
 B)False

Question 5

If the coefficient of correlation between x and y is close to −1.0, which of the following statements is correct?

Accepted Answer

A) There is a strong, positive linear relationship between x and y, where there may or may not be any causal relationship between x and y. 
B) There is a strong, negative linear relationship between x and y, where there must be a causal relationship between x and y. 
C) There is a weak, negative linear relationship between x and y, where there may or may not be any causal relationship between x and y. 
D) There is a strong, negative linear relationship between x and y, where there may or may not be any causal relationship between x and y. 
A) There is a strong, positive linear relationship between x and y, where there may or may not be any causal relationship between x and y. 
B) There is a strong, negative linear relationship between x and y, where there must be a causal relationship between x and y. 
C) There is a weak, negative linear relationship between x and y, where there may or may not be any causal relationship between x and y. 
D) There is a strong, negative linear relationship between x and y, where there may or may not be any causal relationship between x and y.

Question 6

If an estimated regression line has a y-intercept of 10 and a slope of -5, then when x = 0, the estimated value of y is:

Accepted Answer

A) −5 
B) 0 
C) 5 
D) 10 
A) −5 
B) 0 
C) 5 
D) 10

Question 7

The symbol for the sample coefficient of correlation is:

Accepted Answer

A) r. 
B)  $\rho$ . 
C)  $r ^ { 2 }$ . 
D)  $\rho ^ { 2 }$ . 
A) r. 
B)  $\rho$ . 
C)  $r ^ { 2 }$ . 
D)  $\rho ^ { 2 }$ .

Question 8

The variance of the error variable, $\sigma _ { \varepsilon } ^ { 2 }$ , is required to be constant. When this requirement is violated, the condition is called heteroscedasticity.

Accepted Answer

A) True 
 B)False

Question 9

Which value of the coefficient of correlation r indicates a stronger correlation than − 0.85?

Accepted Answer

A) −0.50 
B) 0.75 
C) −0.90 
D) 0.85 
A) −0.50 
B) 0.75 
C) −0.90 
D) 0.85

Question 10

If all the points in a scatter diagram lie on the least squares regression line, then the coefficient of correlation must be:

Accepted Answer

A) 1.0. 
B) -1.0. 
C) either 1.0 or -1.0. 
D) 0.0. 
A) 1.0. 
B) -1.0. 
C) either 1.0 or -1.0. 
D) 0.0.

Question 11

A statistician investigating the relationship between the amount of precipitation (in inches) and the number of car accidents gathered data for 10 randomly selected days. The results are presented below. $$\begin{array} { | c | c | c | } 
\hline \text { Day } & \text { Precipitation } & \text { Number of accidents } \
\hline 1 & 0.05 & 5 \
\hline 2 & 0.12 & 6 \
\hline 3 & 0.05 & 2 \
\hline 4 & 0.08 & 4 \
\hline 5 & 0.10 & 8 \
\hline 6 & 0.35 & 14 \
\hline 7 & 0.15 & 7 \
\hline 8 & 0.30 & 13 \
\hline 9 & 0.10 & 7 \
\hline 10 & 0.20 & 10 \
\hline
\end{array}$$ Determine the coefficient of determination and discuss what its value tells you about the two variables.

Accepted Answer

@#IMG-DLM& 0.893, which means that 89.3%

Question 12

A professor of economics wants to study the relationship between income y (in $1000s) and education x (in years). A random sample of eight individuals is taken and the results are shown below. $$\begin{array} { | l | c | c | c | c | c | c | c | c | } 
\hline \text { Education } & 16 & 11 & 15 & 8 & 12 & 10 & 13 & 14 \
\hline \text { Income } & 58 & 40 & 55 & 35 & 43 & 41 & 52 & 49 \
\hline
\end{array}$$ Conduct a test of the population coefficient of correlation to determine at the 5% significance level whether a linear relationship exists between years of education and income.

Accepted Answer

H_o: F1F1F1S1F1F1F10 = 0 H_A: F1F

Question 13

A regression analysis between sales (in $1000) and advertising (in $100) yielded the least squares line $\hat { y }$ = 77 +8x. This implies that if advertising is $600, then the predicted amount of sales (in dollars) is $4877.

Accepted Answer

A) True 
 B)False

If the sum of squared residuals is zero, then the:

Which of the following statements best describes why a linear regression is also called a least squares regression model?

When the actual values y of a dependent variable and the corresponding predicted values $\ddot { p }$ are the same, the standard error of estimate, $S _ { \varepsilon }$ , will be -1.0.

A direct relationship between an independent variable x and a dependent variably y means that x and y move in the same directions.

If the coefficient of correlation between x and y is close to −1.0, which of the following statements is correct?

If an estimated regression line has a y-intercept of 10 and a slope of -5, then when x = 0, the estimated value of y is:

The symbol for the sample coefficient of correlation is:

The variance of the error variable, $\sigma _ { \varepsilon } ^ { 2 }$ , is required to be constant. When this requirement is violated, the condition is called heteroscedasticity.

Which value of the coefficient of correlation r indicates a stronger correlation than − 0.85?

If all the points in a scatter diagram lie on the least squares regression line, then the coefficient of correlation must be:

A regression analysis between sales (in $1000) and advertising (in $100) yielded the least squares line $\hat { y }$ = 77 +8x. This implies that if advertising is $600, then the predicted amount of sales (in dollars) is $4877.

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Techniques Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference and Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Additional Tests for Nominal Data: Chi-Squared Tests

Multiple Regression

Time-Series Analysis and Forecasting

Index Numbers

Filters

Exam 15: Simple Linear Regression and Correlation

If the sum of squared residuals is zero, then the:

Which of the following statements best describes why a linear regression is also called a least squares regression model?

When the actual values y of a dependent variable and the corresponding predicted values p¨\ddot { p }p¨​ are the same, the standard error of estimate, SεS _ { \varepsilon }Sε​ , will be -1.0.

A direct relationship between an independent variable x and a dependent variably y means that x and y move in the same directions.

If the coefficient of correlation between x and y is close to −1.0, which of the following statements is correct?

If an estimated regression line has a y-intercept of 10 and a slope of -5, then when x = 0, the estimated value of y is:

The symbol for the sample coefficient of correlation is:

The variance of the error variable, σε2\sigma _ { \varepsilon } ^ { 2 }σε2​ , is required to be constant. When this requirement is violated, the condition is called heteroscedasticity.

Which value of the coefficient of correlation r indicates a stronger correlation than − 0.85?

If all the points in a scatter diagram lie on the least squares regression line, then the coefficient of correlation must be:

A regression analysis between sales (in $1000) and advertising (in $100) yielded the least squares line y^\hat { y }y^​ = 77 +8x. This implies that if advertising is $600, then the predicted amount of sales (in dollars) is $4877.

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Techniques Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference and Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Additional Tests for Nominal Data: Chi-Squared Tests

Multiple Regression

Time-Series Analysis and Forecasting

Index Numbers

Filters

When the actual values y of a dependent variable and the corresponding predicted values $\ddot { p }$ are the same, the standard error of estimate, $S _ { \varepsilon }$ , will be -1.0.

The variance of the error variable, $\sigma _ { \varepsilon } ^ { 2 }$ , is required to be constant. When this requirement is violated, the condition is called heteroscedasticity.

A regression analysis between sales (in $1000) and advertising (in $100) yielded the least squares line $\hat { y }$ = 77 +8x. This implies that if advertising is $600, then the predicted amount of sales (in dollars) is $4877.